SUPLEMENTARY CHAPTER 1 An Introduction to Digital Logic

SUPLEMENTARY CHAPTER 1: An Introduction to Digital Logic § The Architecture of Computer Hardware and Systems Software: An Information Technology Approach § 3 rd Edition, Irv Englander § John Wiley and Sons 2003 § Linda Senne, Bentley College § Wilson Wong, Bentley College

Integrated Circuits § The building blocks of computers § Designed for specialized functions § Examples: the CPU, bus interface, memory management unit § Transistors: primary components of ICs § Motorola MPC 7400 Power. PC modules: 6. 5 million transistors in less than ½ in 2 Supplementary Chapter 1 Digital Computer Logic 2

Transistors § Boolean algebra: basis for computer logic design § Transistors: means for implementing Boolean algebra § Switches: on/off to represent the 0’s and 1’s of binary digital circuits § Combined to form logic gates Supplementary Chapter 1 Digital Computer Logic 3

Digital Circuits § Combinatorial logic § Results of an operation depend only on the present inputs to the operation § Uses: perform arithmetic, control data movement, compare values for decision making § Sequential logic § Results depend on both the inputs to the operation and the result of the previous operation § Uses: counter Supplementary Chapter 1 Digital Computer Logic 4

Boolean Algebra § Rules that govern constants and variables that can take on 2 values § True/false; on/off; yes/no; 0/1 § Boolean logic § Rules for handling Boolean constants and variables § 3 fundamental operations: AND, OR and NOT § Truth Table: specifies results for all possible input combinations Supplementary Chapter 1 Digital Computer Logic 5

Boolean Operators § AND § Result TRUE if and only if both input operands are true § C=A B § INCLUSIVE-OR § Result TRUE if any input operands are true § C=A+B Supplementary Chapter 1 Digital Computer Logic A B C 0 0 1 1 1 A B C 0 0 1 1 1 0 1 1 6

Boolean Operators § NOT § Result TRUE if single input value is FALSE § C=A Supplementary Chapter 1 Digital Computer Logic A C 0 1 1 0 7

Boolean Operators § EXCLUSIVE-OR § Result TRUE if either A or B is TRUE but not both § C=A⊕B § Can be derived from INCLUSIVE-OR, AND and NOT p A B C 0 0 1 1 1 0 A ⊕ B = (A + B) ( A B ) A xor B equals A or B but not both A and B p A ⊕ B = (A B ) + ( B A ) A xor B = either A and not B or B and not A Supplementary Chapter 1 Digital Computer Logic 8

Boolean Algebra Operations § Valid for INCLUSIVE-OR, AND, XOR § Associative p A + ( B + C ) = ( A + B ) + C § Distributive p A ( B + C ) = A B + A C § Commutative p A + B = B + A § De. Morgan’s Theorems § A + B = A B § A B = A + B Supplementary Chapter 1 Digital Computer Logic 9

Gates and Combinatorial Logic § Many computer functions defined in terms of Boolean equations § Example: sum of 2 single binary digit numbers § Truth table for sum Truth table for carry XOR AND A B C 0 0 0 0 1 1 0 1 1 1 Supplementary Chapter 1 Digital Computer Logic 10

Computer Implementation § Gates or logical gates § Integrated circuits constructed from transistor switches and other electronic components § VLSI: very large-scale integration Supplementary Chapter 1 Digital Computer Logic 11

Boolean Algebra Implementation § Single type of gate appropriately combined § 2 possibilities § NAND gate: AND operation followed by a NOT operation § NOR gate: INCLUSIVE-OR followed by a NOT operation Note: indicates a NOT operation Supplementary Chapter 1 Digital Computer Logic 12

Selector or Multiplexer § Switch input back and forth between inputs § Logic circuits that make up a computer § are relatively simple but § look complicated because many circuits required Supplementary Chapter 1 Digital Computer Logic 13

Half-Adder Supplementary Chapter 1 Digital Computer Logic 14

Full Adder § Handles possible carry from previous bit § Half adder shown as block to simplify (portion of half adder in Fig. S 1. 11 enclosed in dotted line) § 2 -bit adder contains 32 circuits § Also called ripple adder because the carry ripples through 32 bits Supplementary Chapter 1 Digital Computer Logic 15

Sequential Logic Circuits § Output depends on § Input § Previous state of the circuit § Flip-flop: basic memory element § State table: output for all combinations of input and previous states p Cf. Truth Table Supplementary Chapter 1 Digital Computer Logic 16

Flip-Flop Types with State Tables Supplementary Chapter 1 Digital Computer Logic 17

Register COPY Operation § Uses both sequential and combinatorial logic Supplementary Chapter 1 Digital Computer Logic 18

Steps in a LOAD Instruction Supplementary Chapter 1 Digital Computer Logic 19

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